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Multivariate Reversed Hazard Rates and Inactivity Times of Systems

Author

Listed:
  • Francesco Buono

    (Università degli Studi di Napoli Federico II)

  • Emilio Santis

    (Università La Sapienza)

  • Maria Longobardi

    (Università degli Studi di Napoli Federico II)

  • Fabio Spizzichino

    (Università La Sapienza)

Abstract

The family of the multivariate conditional hazard rate functions often reveals to be a convenient tool to describe the joint probability distribution of a vector of non-negative random variables (lifetimes) in the absolutely continuous case. Such a tool can have in particular an important role in the study of the behavior of the minima among inter-dependent lifetimes. In this paper we introduce the concept of reversed multivariate conditional hazard rate functions, which extends the one-dimensional notion of reversed hazard rate of a single non-negative random variable. Several basic properties of this concept are proven. In particular, we point out a related role in the study of the behavior of the maximum value among inter-dependent lifetimes. In different applied fields, and in particular in the reliability literature, a remarkable class of dependence models for vectors of lifetimes is related with the load-sharing condition, which can be defined in terms of the multivariate conditional hazard rate functions. In the paper we define the class of reversed load-sharing models, which can be seen as natural extensions to the multivariate case of the univariate inverse exponential distributions. We analyze basic properties of such a class of dependence models. In particular we show a result related to the study of the inactivity time of a coherent system when the joint distribution of the components’ lifetimes is a reversed load-sharing model.

Suggested Citation

  • Francesco Buono & Emilio Santis & Maria Longobardi & Fabio Spizzichino, 2022. "Multivariate Reversed Hazard Rates and Inactivity Times of Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1987-2008, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09905-2
    DOI: 10.1007/s11009-021-09905-2
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    References listed on IDEAS

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